Properties

Genus \(12\)
Quotient Genus \(0\)
Group \(C_{50}\)
Signature \([ 0; 2, 25, 50 ]\)
Generating Vectors \(1\)

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Family Information

Genus: 12
Quotient Genus: 0
Group name: $C_{50}$
Group identifier: [50,2]
Signature: $[ 0; 2, 25, 50 ]$
Conjugacy classes for this refined passport: 2, 18, 47

Jacobian variety group algebra decomposition:$A_{10}\times A_{2}$
Corresponding character(s): 4, 12

Other Data

Hyperelliptic curve(s):Yes
Hyperelliptic involution: (1,26) (2,27) (3,28) (4,29) (5,30) (6,31) (7,32) (8,33) (9,34) (10,35) (11,36) (12,37) (13,38) (14,39) (15,40) (16,41) (17,42) (18,43) (19,44) (20,45) (21,46) (22,47) (23,48) (24,49) (25,50)
Cyclic trigonal curve(s):No

Equation(s) of curve(s) in this refined passport:
  $y^2=x^{25}+1$

Generating Vector(s)

Displaying the unique generating vector for this refined passport.

12.50-2.0.2-25-50.8.1

  (1,26) (2,27) (3,28) (4,29) (5,30) (6,31) (7,32) (8,33) (9,34) (10,35) (11,36) (12,37) (13,38) (14,39) (15,40) (16,41) (17,42) (18,43) (19,44) (20,45) (21,46) (22,47) (23,48) (24,49) (25,50)
  (1,22,19,11,8,5,21,18,15,7,4,25,17,14,6,3,24,16,13,10,2,23,20,12,9) (26,47,44,36,33,30,46,43,40,32,29,50,42,39,31,28,49,41,38,35,27,48,45,37,34)
  (1,34,12,45,23,27,10,38,16,49,3,31,14,42,25,29,7,40,18,46,5,33,11,44,22,26,9,37,20,48,2,35,13,41,24,28,6,39,17,50,4,32,15,43,21,30,8,36,19,47)